Publications

Order by: publication date number of citations

• Entanglement in the quantum Hall fluid of dipoles

  Jackson R. Fliss

  SciPost Phys. 11, 052 (2021) · published 9 September 2021 | Toggle abstract · pdf

  We revisit a model for gapped fractonic order in (2+1) dimensions (a symmetric-traceless tensor gauge theory with conservation of dipole and trace-quadrupole moments described in \cite{Prem:2017kxc}) and compute its ground-state entanglement entropy on $\mathbb R^2$. Along the way, we quantize the theory on open subsets of $\mathbb R^2$ which gives rise to gapless edge excitations that are Lifshitz-type scalar theories. We additionally explore varieties of gauge-invariant extended operators and rephrase the fractonic physics in terms of the local deformability of these operators. We explore similarities of this model to the effective field theories describing quantum Hall fluids: in particular, quantization of dipole moments through a novel compact symmetry leads us to interpret the vacuum of this theory as a dipole condensate atop of which dipoles with fractionalized moments appear as quasi-particle excitations with Abelian anyonic statistics. This interpretation is reflected in the subleading ``topological entanglement" correction to the entanglement entropy. We extend this result to a series of models with conserved multipole moments.

  4 citations

• A time-dependent momentum-resolved scattering approach to core-level spectroscopies

  Krissia Zawadzki, Alberto Nocera, Adrian E. Feiguin

  SciPost Phys. 15, 166 (2023) · published 17 October 2023 | Toggle abstract · pdf

  While new light sources allow for unprecedented resolution in experiments with X-rays, a theoretical understanding of the scattering cross-section is lacking. In the particular case of strongly correlated electron systems, numerical techniques are quite limited, since conventional approaches rely on calculating a response function (Kramers-Heisenberg formula) that is obtained from a perturbative analysis of scattering processes in the frequency domain. This requires a knowledge of a full set of eigenstates in order to account for all intermediate processes away from equilibrium, limiting the applicability to small tractable systems. In this work, we present an alternative paradigm, recasting the problem in the time domain and explicitly solving the time-dependent Schrödinger equation without the limitations of perturbation theory: a faithful simulation of the scattering processes taking place in actual experiments, including photons and core electrons. We show how this approach can yield the full time and momentum resolved Resonant Inelastic X-Ray Scattering (RIXS) spectrum of strongly interacting many-body systems. We demonstrate the formalism with an application to Mott insulating Hubbard chains using the time-dependent density matrix renormalization group method, which does not require a priory knowledge of the eigenstates and can solve very large systems with dozens of orbitals. This approach can readily be applied to systems out of equilibrium without modification and generalized to other spectroscopies.

  4 citations

• Matrix product operator representations for the local conserved quantities of the Heisenberg chain

  Kyoichi Yamada, Kohei Fukai

  SciPost Phys. Core 6, 069 (2023) · published 19 October 2023 | Toggle abstract · pdf

  We present the explicit expressions for the matrix product operator (MPO) representation for the local conserved quantities of the Heisenberg chain. The bond dimension of the MPO grows linearly with the locality of the charges. The MPO has more simple form than the local charges themselves, and their Catalan tree patterns naturally emerge from the matrix products. The MPO representation of local conserved quantities is generalized to the integrable SU(N) invariant spin chain.

  4 citations

• Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

  Roman Rausch, Matthias Peschke, Cassian Plorin, Jürgen Schnack, Christoph Karrasch

  SciPost Phys. 14, 052 (2023) · published 28 March 2023 | Toggle abstract · pdf

  The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions $J$ and antiferromagnetic next-nearest-neighbour interactions $J'$ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations $\left<{\vec{S}_i}\right>$, the spiral can be detected via the connected spin-spin correlations $\left<{\vec{S}_i\cdot\vec{S}_j}\right>-\left<{\vec{S}_i}\right>\cdot\left<{\vec{S}_j}\right>$ between the apical spins. It has a long wavelength that grows with $J'$ and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems. In this work, we are able to accurately treat up to $L=400$ sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowest-energy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.

  4 citations

• Theory of Andreev blockade in a double quantum dot with a superconducting lead

  David Pekker, Po Zhang, Sergey M. Frolov

  SciPost Phys. 11, 081 (2021) · published 22 October 2021 | Toggle abstract · pdf

  A normal metal source reservoir can load two electrons onto a double quantum dot in the spin-triplet configuration. We show that if the drain lead of the dot is a spin-singlet superconductor, these electrons cannot form a Cooper pair and are blockaded on the double dot. We call this phenomenon Andreev blockade because it arises due to suppressed Andreev reflections. We identify transport characteristics unique to Andreev blockade. Most significantly, it occurs for any occupation of the dot adjacent to the superconductor, in contrast with the well-studied Pauli blockade which requires odd occupations. Andreev blockade is lifted if quasiparticles are allowed to enter the superconducting lead, but it should be observable in the hard gap superconductor-semiconductor devices. A recent experiment tests this model and finds support for several predictions made here [P. Zhang, H. Wu, J. Chen, S. A. Khan, P. Krogstrup, D. Pekker, and S. M. Frolov, arXiv:2102.03283 (2021)]. Andreev blockade should be considered in the design of topological quantum circuits, hybrid quantum bits and quantum emulators.

  4 citations

• The classical Heisenberg model on the centred pyrochlore lattice

  Rajah P. Nutakki, Ludovic D. C. Jaubert, Lode Pollet

  SciPost Phys. 15, 040 (2023) · published 1 August 2023 | Toggle abstract · pdf

  The centred pyrochlore lattice is a novel geometrically frustrated lattice, realized in the metal-organic framework Mn(ta)$_2$ [Phys. Rev. Research 5, L022018 (2023)] where the basic unit of spins is a five site centred tetrahedron. Here, we present an in-depth theoretical study of the $J_1-J_2$ classical Heisenberg model on this lattice, using a combination of mean-field analytical methods and Monte Carlo simulations. We find a rich phase diagram with low temperature states exhibiting ferrimagnetic order, partial ordering, and a highly degenerate spin liquid with distinct regimes of low temperature correlations. We discuss in detail how the regime displaying broadened pinch points in its spin structure factor is consistent with an effective description in terms of a fluid of interacting charges. We also show how this picture holds in two dimensions on the analogous centred kagome lattice and elucidate the connection to the physics of thin films in ($d+1$) dimensions. Furthermore, we show that a Coulomb phase can be stabilized on the centred pyrochlore lattice by the addition of further neighbour couplings. This demonstrates the centred pyrochlore lattice is an experimentally relevant geometry which naturally hosts emergent gauge fields in the presence of charges at low energies.

  4 citations

• Conjectures about the structure of strong- and weak-coupling expansions of a few ground-state observables in the Lieb-Liniger and Yang-Gaudin models

  Guillaume Lang

  SciPost Phys. 7, 055 (2019) · published 23 October 2019 | Toggle abstract · pdf

  In this paper, we apply experimental number theory to two integrable quantum models in one dimension, the Lieb-Liniger Bose gas and the Yang-Gaudin Fermi gas with contact interactions. We identify patterns in weak- and strong-coupling series expansions of the ground-state energy, local correlation functions and pressure. Based on the most accurate data available in the literature, we make a few conjectures about their mathematical structure and extrapolate to higher orders.

  4 citations

• Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

  Mostafa Tanhayi Ahari, Sumanta Bandyopadhyay, Zohar Nussinov, Alexander Seidel, Gerardo Ortiz

  SciPost Phys. 15, 043 (2023) · published 2 August 2023 | Toggle abstract · pdf

  We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor $\nu=2/3$. The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the "DNA" of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body $M$-clustering property within any given number of Landau levels, that is, wave functions with $M$th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the $M=3$ case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.

  4 citations

• Free fermions with dephasing and boundary driving: Bethe Ansatz results

  Vincenzo Alba

  SciPost Phys. Core 8, 011 (2025) · published 30 January 2025 | Toggle abstract · pdf

  By employing the Lindblad equation, we derive the evolution of the two-point correlator for a free-fermion chain of length $L$ subject to bulk dephasing and boundary losses. We use the Bethe Ansatz to diagonalize the Liouvillian $\mathcal{L}^{(2)}$ governing the dynamics of the correlator. The majority of its eigenvalues are complex. Precisely, $L(L-1)/2$ complex eigenvalues do not depend on dephasing, apart from a trivial shift. The remaining complex levels are perturbatively related to the dephasing-independent ones for large $L$. The long-time dynamics is governed by a band of real eigenvalues, which contains an extensive number of levels. They give rise to diffusive scaling at intermediate times, when boundaries can be neglected. Moreover, they encode the breaking of diffusion at asymptotically long times. Interestingly, for large loss rate two boundary modes appear in the spectrum. The real eigenvalues correspond to string solutions of the Bethe equations, and can be treated effectively for large chains. This allows us to derive compact formulas for the dynamics of the fermionic density. We check our results against exact diagonalization, finding perfect agreement.

  4 citations

• Detect axial gauge fields with a calorimeter

  Matteo Baggioli, Maxim N. Chernodub, Karl Landsteiner, Maria A. H. Vozmediano

  SciPost Phys. Core 3, 013 (2020) · published 2 December 2020 | Toggle abstract · pdf

  Torsional strain in Weyl semimetals excites a unidirectional chiral density wave propagating in the direction of the torsional vector. This gapless excitation, named the chiral sound wave, is generated by a particular realization of the axial anomaly via the triple-axial (AAA) anomalous diagram. We show that the presence of the torsion-generated chiral sound leads to a linear behavior of the specific heat of a Weyl semimetal and to an enhancement of the thermal conductivty at experimentally accessible temperatures. We also demonstrate that such an elastic twist lowers the temperature of the sample, thus generating a new, anomalous type of elasto-calorific effect. Measurements of these thermodynamical effects will provide experimental verification of the exotic triple-axial anomaly as well as the reality of the elastic pseudomagnetic fields in Weyl semimetals.

  4 citations